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FRANKFURT - Major central banks around the world moved yesterday to remove doubts about the ability of European banks to borrow dollars, opening new lines of credit to institutions for longer periods than before.

The European Central Bank said it would allow banks to borrow dollars for up to three months, instead of just for one week as before.

The ECB said it was acting in coordination with the US Federal Reserve, the Bank of England, the Bank of Japan, and the Swiss National Bank.

Shares of European banks, especially French banks, have fallen sharply in recent weeks amid reports that US money market funds have been reluctant to lend to them, because of fear they are vulnerable to losses on their holdings of Greek bonds.

Two of France’s biggest banks, Societe Generale and Credit Agricole, were downgraded a notch Wednesday by Moody’s Investors Service.

The new liquidity moves will be in addition to the ECB’s current weekly dollar swaps, the bank said.

The ECB action came on the same day that Spain pulled off a successful - if expensive - bond sale, and a top official of the ECB rejected criticism from Germany that the bank has exceeded its authority by aiding Greece and other beleaguered countries in the euro area.

A day after the leaders of France and Germany promised to support Greece’s continued membership in the currency bloc, the German chancellor, Angela Merkel, adopted a scolding tone, telling indebted countries to “do their homework.’’

Merkel promised Germany would defend the euro, but insisted that troubled countries are still responsible for tackling their own problems.

“It is in our fundamental interest, as the largest economy in Europe, to make our contribution in order to ensure the future of the euro,’’ she said. But she rejected what she called a “debt union’’ in Europe.

Speaking in Rome, Lorenzo Bini Smaghi, a member of the ECB executive board, said it would be a mistake to leave countries at the mercy of financial markets, which he said are not functioning properly anyway.

He said criticisms of the bank are “the result of inadequate economic analysis, of insufficient knowledge of the crisis in which we find ourselves and of anxiety resulting from experiences in the distant past that are not relevant to the current situation’’ - an apparent reference to the hyperinflation of the 1920s, which still influences German attitudes toward price stability.